Trajectory tracking control has been studied extensively and applied to wide range of platforms, including small unmanned vehicles, helicopters, transport-class aircraft in the context of next-generation air transport, and resilient aircraft control. Tracking on guided munitions and missile systems in particular poses significant technical challenges because of inherent uncertainties, nonlinearity of the systems, and demanding performance requirements for tracking highly maneuverable targets.
Gain scheduling has been used for trajectory tracking of autonomous vehicles, though gain-scheduling approaches are often used ad-hoc in the design. Trajectory Linearization Control (TLC) has been described as including consisting of a nonlinear, dynamic pseudo-inversion based open-loop nominal controller, together with a linear, time-varying (LTV) feedback controller to exponentially stabilize the linearized tracking error dynamics. This approach was applied to a multiple-input, multiple-out (MIMO) system, which presents a trajectory linearization approach on a roll-yaw autopilot for a non-axisymmetric missile model. TLC controllers have also been designed for a three degree-of-freedom (3DOF) control of a reusable launch vehicle, a 3DOF longitudinal control of a hypersonic scramjet dynamics model, and a six degree-of-freedom (6DOF) control of a vertical take-off and landing (VTOL) aircraft model.
Control Lyapunov function (CLF) approaches have been used for nonlinear controller design for the trajectory tracking problem. Receding horizon control (RHC) and model predictive control (MPC) approaches have also been evaluated. CLF has been used to construct universal stabilizing formulas for various constrained input cases: for instance, in a system with control inputs bounded to a unit sphere, and a system with positive bound scalar control inputs. The CLF approach is applied to constrained nonlinear trajectory tracking control for an unmanned aerial vehicle (UAV) outside of an established longitudinal and lateral mode autopilot, where inputs are subject to rate constraints. Control input that satisfies the tracking requirements is selected from a feasible set of inputs which was generated through a CLF designed for the input constraints. This approach was extended to perform nonlinear tracking utilizing backstepping techniques to develop a velocity and roll angle control law for a fixed wing UAV, and unknown autopilot constants are identified through parameter adaptation. A similar backstepping approach has been utilized on trajectory tracking control for helicopters. A backstepping controller has been compared to a classical nonlinear dynamic inversion control approach for a path angle trajectory controller, where model selection was found to impact performance of the inversion control, but the backstepping approach led to a complex control structure that was difficult to test with limited guarantee of stability.
Adaptive control approaches have also been studied in the literature to handle uncertainty. In particular, approaches utilizing neural networks seem to be an effective tool to control a wide class of complex nonlinear systems with incomplete model information. Dynamic neural networks are utilized for adaptive nonlinear identification trajectory tracking, where a dynamic Lyapunov-like analysis is utilized to determine stability conditions utilizing algebraic and differential Riccati equations. Dynamic inversion control augmented by an on-line neural network has been applied to several platforms, including guided munitions and damaged aircraft, and has been applied to a trajectory following flight control architecture.
Because of the highly nonlinear and time-varying nature of flight dynamics in maneuvering trajectory tracking, conventional flight controllers typically rely on gain-scheduling a bank of controllers designed using linear time-invariant (LTI) system theory. Gain-scheduling controllers suffer from inherent slowly-time-varying and benign nonlinearity constraints, and the controller design and tuning are highly trajectory dependent. Modern nonlinear control techniques such as feedback linearization and dynamic inversion alleviate these limitations by cancelling the nonlinearity via a coordinate transformation and state feedback, or by constructing a dynamic (pseudo) inverse of the nonlinear plant. LTI tracking error dynamics can be formulated after the nonlinear cancellation, and controlled by LTI controllers. A drawback of this type of control scheme is that the nonlinearity cancellation is accomplished in the LTI control loop. Consequently, imperfect cancellation because of sensor dynamics or modeling errors result in nonlinear dynamics that are not compensated for by the LTI controller design, and cannot be effectively accommodated by the LTI controller.